I have a MacBook and it has been giving me a weird issue since today morning. I have a WiFi at home and when I booted up my laptop it showed connected to my Wi-Fi network even when the router was switched off.
I tried rebooting my laptop and turning the AirPort on and off, but I faced the same issue. It still showed connected to the wifi network that had been off for the past couple of hours.
The net did start to work when I switched on the router but I still can't figure out why this was happening.